$\beta$-function of the level-zero Gross-Neveu model

Abstract

We explain that the supersymmetric $C{P}^{n-1}$ sigma model is directly related to the level-zero chiral Gross-Neveu (cGN) model. In particular, beta functions of the two theories should coincide. This is consistent with the one-loop-exactness of the $C{P}^{n-1}$ beta function and a conjectured all-loop beta function of cGN models. We perform an explicit four-loop calculation on the cGN side and discuss the renormalization scheme dependence that arises.

36 pages, 8 figures

References in corpus (12)

• Four loop renormalization of the Gross-Neveu model
• The NSVZ beta-function in supersymmetric theories with different regularizations and renormalization prescriptions
• Principal Chiral Model on Superspheres
• Four loop MSbar mass anomalous dimension in the Gross-Neveu model
• Flag manifold sigma models: spin chains and integrable theories
• N=(0, 2) Deformation of (2, 2) Sigma Models: Geometric Structure, Holomorphic Anomaly and Exact Beta Functions
• Sigma models as Gross-Neveu models
• Quantum flag manifold $\sigma$-models and Hermitian Ricci flow
• The three-loop anomalous dimension and the four-loop $\beta$-function for $\mathcal{N}=1$ SQED regularized by higher derivatives
• The $\mathsf{C}{\mathsf{P}}^{\mathsf{n}-1}$-model with fermions: a new look
• Comments on the NSVZ $\beta$ Functions in Two-dimensional $\mathcal{N}=(0,2)$ Supersymmetric Models
• Integrable sigma models on Riemann surfaces